The authors consider the interior Dirichlet problem for Laplace’s equation on planar domains with corners. They provide a complete analysis of a natural method of Nyström type based on the global Gauss–Lobatto quadrature rule, in order to approximate the solution of the corresponding double layer boundary integral equation. Mellin-type integral operators are involved and, as usual, a modification of the method close to the corners is needed. A new modification is proposed and the convergence and stability of the “modified” quadrature method are proved. Some numerical tests are also included.
|Titolo:||A Nyström method for a boundary integral equation related to the Dirichlet problem on domains with corners|
|Data di pubblicazione:||2015|
|Tipologia:||1.1 Articolo in rivista|